Related papers: Optimal dynamical stabilization
When studying out-of-equilibrium systems, one often excites the dynamics in some degrees of freedom while removing the excitation in others through damping. In order for the system to converge to a statistical steady state, the dynamics…
Locomotion in the real world involves unexpected perturbations, and therefore requires strategies to maintain stability to successfully execute desired behaviours. Ensuring the safety of locomoting systems therefore necessitates a…
While classical control theory assumes that the controller has access to measurements of the entire state (or output) at every time instant, this paper investigates a setting where the feedback controller can only access a randomly selected…
Steady state fluctuation relations for dynamical systems are commonly derived under the assumption of some form of time-reversibility and of chaos. There are, however, cases in which they are observed to hold even if the usual notion of…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…
Can we conclude the stability of an unknown dynamical system from the knowledge of a finite number of snapshots of trajectories? We tackle this black-box problem for switched linear systems. We show that, for any given random set of…
We introduce a new notion of the stability of computations, which holds under post-processing and adaptive composition. We show that the notion is both necessary and sufficient to ensure generalization in the face of adaptivity, for any…
Motivated by questions in biology, we investigate the stability of equilibria of the dynamical system $\mathbf{x}^{\prime}=P(t)\nabla f(x)$ which arise as critical points of $f$, under the assumption that $P(t)$ is positive semi-definite.…
For stochastic systems with nonvanishing noise, i.e., at the desired state the noise port does not vanish, it is impossible to achieve the global stability of the desired state in the sense of probability. This bad property also leads to…
Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way. Several open dynamical systems can be…
A major limitation of the classical control theory is the assumption that the state space and its dimension do not change with time. This prevents analyzing and even formalizing the stability and control problems for open multi-agent…
There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…
The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…
Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially…
Metastability in open system dynamics describes the phenomena of initial relaxation to longlived metastable states before decaying to the asymptotic stable states. It has been predicted in continuous-time stochastic dynamics of both…
This work studies the stabilization for a periodic parabolic system under perturbations in the system conductivity. A perturbed system does not have any periodic solution in general. However, we will prove that the perturbed system can…
The paper shows sufficiency conditions for stability of continuous periodic orbits under phase uncertainty. Phase based uncertainty is a trait of bipedal walking robots, where the desired trajectories are parameterized by a monotonous…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…
In this paper we introduce the notion of a patient first-mean stable system. Such systems are switched systems that are first-mean stable meaning that they converge to a globally attracting fixed point on average. They are also patient so…
Self-stabilization is a strong property that guarantees that a network always resume correct behavior starting from an arbitrary initial state. Weaker guarantees have later been introduced to cope with impossibility results: probabilistic…